If you've ever used steel wool on pots & pans, you'll recognize how quickly they turn to rust.  An easy way to avoid steel wool rust is, that when you are finished with it - store it in a small clay flower pot.  The clay in the pot will draw the water out of the steel.wool/brillo and it won't get rusty.

You can even have the kids decorate the pot to match the colors in your kitchen (or just for a quick cute craft).  Generally you can store the little pot under your sink in the clay pot - and it will be rust-free when you go to use it again.

Another tip with using brillo pads or steel wool in the kitchen - is to cut the original piece in half.  Unless you are washing a giant Turkey pan, you really only need half, so why not stretch your eco-dollar further?